The couple announced their engagement in April 2011 and welcomed their son Bingham Hawn in July.
However, Hawn told Us Weekly that the pair are not rushing into marriage.
"There's no prepping for a wedding," she said.
"[Hudson's] very happy. She's a great mum, the baby's beautiful, and they'll get married when they're ready."
Rumours that Hudson and Bellamy had tied the knot began to circulate last month after Hawn said: "When my daughter Kate married an English rock star it didn't worry me."
However, Hawn later clarified that the pair had not yet wed, tweeting that the reporter she spoke to had "twisted the truth".